




def lowerCamelCase__  (     _lowercase					,		_lowercase = False ):

     '''simple docstring'''


     if n == 2:
          return True
     if not n % 2 or n < 2:
          return False
     if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
          return False
     if n > 3317044064679887385961981 and not allow_probable:
          raise ValueError(
              '''Warning: upper bound of deterministic test is exceeded. '''
              '''Pass allow_probable=True to allow probabilistic test. '''
              '''A return value of True indicates a probable prime.''' )
     # array bounds provided by analysis
     UpperCAmelCase_     :				Tuple  =     [
         2047,
         1373653,
         25326001,
         3215031751,
         2152302898747,
         3474749660383,
         341550071728321,
         1,
         3825123056546413051,
         1,
         1,
         318665857834031151167461,
         3317044064679887385961981,
     ]

     UpperCAmelCase_     :				Dict  =     [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
     for idx, _p in enumerate(_lowercase					,		1 ):
          if n < _p:
               # then we have our last prime to check
               UpperCAmelCase_     :				Dict  =     primes[:idx]
               break
     UpperCAmelCase_,       UpperCAmelCase_     :				Dict  =     n - 1, 0
     # break up n -1 into a power of 2 (s) and
     # remaining odd component
     # essentially, solve for d * 2 ** s == n - 1
     while d % 2 == 0:
          d //= 2
          s += 1
     for prime in plist:
          UpperCAmelCase_     :				Any  =     False
          for r in range(_lowercase ):
               UpperCAmelCase_     :				Optional[int]  =     pow(_lowercase					,		d * 2**r					,		_lowercase )
               # see article for analysis explanation for m
               if (r == 0 and m == 1) or ((m + 1) % n == 0):
                    UpperCAmelCase_     :				int  =     True
                    # this loop will not determine compositeness
                    break
          if pr:
               continue
          # if pr is False, then the above loop never evaluated to true,
          # and the n MUST be composite
          return False
     return True







def lowerCamelCase__  (     ):

     '''simple docstring'''


     assert not miller_rabin(561 )
     assert miller_rabin(563 )
     # 2047

     assert not miller_rabin(838201 )
     assert miller_rabin(838207 )
     # 1_373_653

     assert not miller_rabin(17316001 )
     assert miller_rabin(17316017 )
     # 25_326_001

     assert not miller_rabin(3078386641 )
     assert miller_rabin(3078386653 )
     # 3_215_031_751

     assert not miller_rabin(1713045574801 )
     assert miller_rabin(1713045574819 )
     # 2_152_302_898_747

     assert not miller_rabin(2779799728307 )
     assert miller_rabin(2779799728327 )
     # 3_474_749_660_383

     assert not miller_rabin(113850023909441 )
     assert miller_rabin(113850023909527 )
     # 341_550_071_728_321

     assert not miller_rabin(1275041018848804351 )
     assert miller_rabin(1275041018848804391 )
     # 3_825_123_056_546_413_051

     assert not miller_rabin(79666464458507787791867 )
     assert miller_rabin(79666464458507787791951 )
     # 318_665_857_834_031_151_167_461

     assert not miller_rabin(552840677446647897660333 )
     assert miller_rabin(552840677446647897660359 )
     # 3_317_044_064_679_887_385_961_981
     # upper limit for probabilistic test


if __name__ == "__main__":
     test_miller_rabin()
import time
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch, torch_device

from ..test_modeling_common import ids_tensor


if is_torch_available():
     import torch

     from transformers.generation import (
         MaxLengthCriteria,
         MaxNewTokensCriteria,
         MaxTimeCriteria,
         StoppingCriteriaList,
         validate_stopping_criteria,
     )
@require_torch
class SCREAMING_SNAKE_CASE_		(      unittest.TestCase		):







   def 						lowerCamelCase_	(     self						:						Tuple   ,   lowerCamelCase_						:						Tuple				):





    """simple docstring"""


    UpperCamelCase			  =      3
    UpperCamelCase			  =      250

    UpperCamelCase			  =      ids_tensor((batch_size, length)   ,   lowerCamelCase_				)
    UpperCamelCase			  =      torch.ones((batch_size, length)   ,   device=lowerCamelCase_   ,   dtype=torch.float				) / length
    return input_ids, scores







   def 						lowerCamelCase_	(     self						:						Tuple				):





    """simple docstring"""


    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(5				)

    UpperCamelCase			  =      StoppingCriteriaList(
        [
            MaxLengthCriteria(max_length=10				),
            MaxTimeCriteria(max_time=0.1				),
        ]				)

    self.assertFalse(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(9				)
    self.assertFalse(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(10				)
    self.assertTrue(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)







   def 						lowerCamelCase_	(     self						:						str				):





    """simple docstring"""


    UpperCamelCase			  =      MaxLengthCriteria(max_length=10				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(5				)
    self.assertFalse(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(9				)
    self.assertFalse(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(10				)
    self.assertTrue(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)







   def 						lowerCamelCase_	(     self						:						str				):





    """simple docstring"""


    UpperCamelCase			  =      MaxNewTokensCriteria(start_length=5   ,   max_new_tokens=5				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(5				)
    self.assertFalse(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(9				)
    self.assertFalse(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(10				)
    self.assertTrue(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase			  =      StoppingCriteriaList([criteria]				)
    self.assertEqual(criteria_list.max_length   ,   10				)







   def 						lowerCamelCase_	(     self						:						Optional[int]				):





    """simple docstring"""


    UpperCamelCase  ,     UpperCamelCase			  =      self._get_tensors(5				)

    UpperCamelCase			  =      MaxTimeCriteria(max_time=0.1				)
    self.assertFalse(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)

    UpperCamelCase			  =      MaxTimeCriteria(max_time=0.1   ,   initial_timestamp=time.time() - 0.2				)
    self.assertTrue(criteria(lowerCamelCase_   ,   lowerCamelCase_				)				)







   def 						lowerCamelCase_	(     self						:						str				):





    """simple docstring"""


    validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10				)]				)   ,   10				)

    with self.assertWarns(lowerCamelCase_				):
     validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10				)]				)   ,   11				)

    UpperCamelCase			  =      validate_stopping_criteria(StoppingCriteriaList()   ,   11				)

    self.assertEqual(len(lowerCamelCase_				)   ,   1				)
